There is Vampiric Companion from Blood of the Night, and Vampiric Animal companion from the Rivals book.
To answer your question, it makes the most sense to apply the Celestial Feat first then the Undead feat. Because it makes little sense to have a live undead. But an Undead Companion could be Undead (Augmented Magical Beast)
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Vampire is a template so Undead should trump. The hierarchy of types (slightly modified from 3.5s Savage Species) should be:
Tier 1
Animal, Humanoid, Vermin
Tier 2
Magical Beast, Monstrous Humanoid
Tier 3
Fey
Tier 4
Dragon
Tier 5
Abberation
Tier 6
Plant, Ooze
Tier 7
Construct, Outsider, Undead
So augmented creatures can go up tiers, but never down. So once a creature is a Construct, for example, it cannot be augmented to be anything else unless a template (or other effect) specifically says otherwise. All subtypes are retained.
The game wasn't made for this amount of bending.
As it is applying a template for intents and purposes, the last feat taken takes over.
Vampire is a template so Undead should trump. The hierarchy of types (slightly modified from 3.5s Savage Species) should be:
Tier 1
Animal, Humanoid, VerminTier 2
Magical Beast, Monstrous HumanoidTier 3
FeyTier 4
DragonTier 5
AbberationTier 6
Plant, OozeTier 7
Construct, Outsider, UndeadSo augmented creatures can go up tiers, but never down. So once a creature is a Construct, for example, it cannot be augmented to be anything else unless a template (or other effect) specifically says otherwise. All subtypes are retained.
Pathfinder isn't 3.5 (which is something that constantly is reinforced with various little rules) so the savage species table holds no sway on the current rule set. Barring a restriction in the feat write up/template both the magical beast and undead 'template' and type changes get applied.
Pathfinder isn't 3.5
Savage Species is actually 3.0, not 3.5. Its still good for suggestions, but not so keen for rules. That said, its likely they didn't think you would take both feats(like cheapy said!) so its left up to your GM. Its harder to imagine a creature going from undead to magical beast than magical beast to undead, imo, but hey, whatever works for a party.
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Here is the Dhampir feat:
Just as your undead existence mocks nature, so too are you granted a twisted companion that reflects the vile nature of vampirism.
Prerequisite: Dhampir or vampire, nongood alignment, 10 levels in a class that grants a familiar or animal companion.
Benefit: Your animal companion or familiar's type changes to “undead.” The creature gains your vampire or dhampir weaknesses and fast healing 5.
If you are a vampire, the creature also gains the following abilities, depending on what type of vampire you are.
Jiang-Shi: If the creature is adjacent to you or you are sharing a square, it gains the benefit of your prayer scroll ability. The creature crumbles into dust if destroyed (just like a jiang-shi), but is not permanently destroyed unless measures are taken that would destroy a jiang-shi.
Moroi: If the creature is adjacent to or in your square when you assume gaseous form, it transforms with you and follows you; its transformation ends when yours does. If reduced to 0 hit points, it is forced into gaseous form and must return to your coffin to reform (or the foot of your coffin if it cannot fit within it).
Nosferatu: If the creature is adjacent to or in your square when you assume swarm form, it transforms with you and follows you; its transformation ends when yours does. The creature can climb as if using spider climb, even if its anatomy is not suitable for climbing (such as a horse).
Vetala: The creature may use malevolence and possession as if it were a vetala, but by touch and only affecting creatures or corpses that are the same type of creature as the animal companion or familiar (such as bear, horse, or snake). If reduced to 0 hit points in combat, the creature is helpless and its fast healing ceases to function for 1 hour (additional damage or desecration has no effect); after 1 hour it regains 1 hit point and is no longer helpless, and its fast healing resumes. It can be permanently destroyed as if it were a vetala.
Special: If your animal companion or familiar is destroyed, dismissed, or lost, you may apply the effects of this feat to the replacement creature. If you are destroyed, the creature retains its undead type but loses all other special abilities from this feat. If you have more than one animal companion or familiar, choose one of them when you select this feat and apply its effects to that creature. You may select this feat more than once. Each time you select the feat, it applies to a different animal companion or familiar.
Pathfinder isn't 3.5Savage Species is actually 3.0, not 3.5. Its still good for suggestions, but not so keen for rules. That said, its likely they didn't think you would take both feats(like cheapy said!) so its left up to your GM. Its harder to imagine a creature going from undead to magical beast than magical beast to undead, imo, but hey, whatever works for a party.
And 3.5 built upon the 3.0 rule set and as I recall the 'type pyramid' stood in 3.5 as was.
Point being those are rules from a different but very similar rule set, so they mean nothing until Paizo decides to cover the issue, house rule as you want.
The weaknesses thing is really up to your DM. And any freeform game can have areas it can be bent more than intended. But as i said earlier it makes sense to add Undead at the end.
3.5 rulings, and even 3.0 rulings, are a perfectly valid source of interpretation, as long as there are no later changes that invalidate the earlier rulings.
Actual courts of law do this kind of thing all the time.
And 3.5 built upon the 3.0 rule set and as I recall the 'type pyramid' stood in 3.5 as was.
Point being those are rules from a different but very similar rule set, so they mean nothing until Paizo decides to cover the issue, house rule as you want.
Important to remember there are differences though, so best to merit 3.0 with what it did and 3.5 for what it did if you can. Also important to remember Pathfinder was built on 3.5, there's quiet a bit of copy pasta and it can be pretty safe to use 3.5 things rules as guidelines, or at least suggestions. I also did say it was houserule territory later on anyway.